# Problem: The bacterium Escherichia coli (or E. coli) is a single- celled organism that lives in the gut of healthy humans and animals. When grown in a uniform medium rich in salts and amino acids, these bacteria swim along zig-zag paths at a constant speed of 20 μm/s. The figure shows the trajectory of an E. coli as it moves from point A to point E. Each segment of the motion can be identified by two letters, such as segment BC.For the segment AB in the bacterium's trajectory, calculate the x component of its velocity.

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###### FREE Expert Solution

The x-component of velocity in AB:

$\overline{){{\mathbf{v}}}_{\mathbf{A}\mathbf{B}\mathbf{x}}{\mathbf{=}}\frac{\mathbf{A}{\mathbf{B}}_{\mathbf{x}}}{{\mathbf{t}}_{\mathbf{x}}}}$

The length AB is given by:

$\begin{array}{rcl}\mathbf{A}\mathbf{B}& \mathbf{=}& \sqrt{\mathbf{A}{{\mathbf{B}}_{\mathbf{x}}}^{\mathbf{2}}\mathbf{+}\mathbf{A}{{\mathbf{B}}_{\mathbf{y}}}^{\mathbf{2}}}\\ & \mathbf{=}& \sqrt{{\mathbf{50}}^{\mathbf{2}}\mathbf{+}{\mathbf{10}}^{\mathbf{2}}}\end{array}$

AB = 50.99 μm

The angle between AB and the positive x-axis can be found from the graph as:

###### Problem Details

The bacterium Escherichia coli (or E. coli) is a single- celled organism that lives in the gut of healthy humans and animals. When grown in a uniform medium rich in salts and amino acids, these bacteria swim along zig-zag paths at a constant speed of 20 μm/s. The figure shows the trajectory of an E. coli as it moves from point A to point E. Each segment of the motion can be identified by two letters, such as segment BC.

For the segment AB in the bacterium's trajectory, calculate the x component of its velocity.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Motion in 2D concept. If you need more Motion in 2D practice, you can also practice Motion in 2D practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Lewis' class at NCSU.